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Cascades of Secondary Particles in High Voltage Accelerators

A very simplified system for high voltage test is studied, considering reason for voltage holding failures which are not covered by conventional and local design criteria. A first understanding of the problem is obtained by solving the electrostatic potential in a 2D axis symmetric geometry, considering in detail the electrode shapes, and following a cascade of particle between opposite electrodes. Very specific attractors were found for the impact points; physical reason is that the highly non uniform electric field may focus, defocus or move the discharge. A second analysis takes into account the spread of the reemitted particle velocity and a consequent 3D motion. Solution of a Fokker Planck style equation for the impact point confirms the existence of hot spots.